= 7 Consider the following model, where r = 0, and a dividend of 1 unit of а currency is paid at time 1.5. * الا W2 W3 S

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= 7 Consider the following model, where r = 0, and a dividend of 1 unit of а currency is paid at time 1.5. * الا W2 W3 S(0,w) S(1,w)* S(2,w)* 0 6 9 11 6 9 7 6 4. 7 6 4 1 ولا (a) Calculate the risk-neutral probabilities at each node of the infor- mation tree. (Remember to put back in the dividend first.) (b) Calculate the value at each node of an American call option with exercise price K = 5 and hence deduce the premium paid at time 0. =